Naik's wife Vijaya and an aide died in the road accident which occurred on Monday when their car met with the accident near Ankola in Uttar Kannada district, while he was returning to home state Goa from Dharmasthala in Karnataka.
Naik, the BJP MP from North Goa, was later shifted to the GMCH.
Sawant said the condition of the Union minister was critical earlier, but now he is stable".
"A team of doctors led by Dean of GMCH Dr Shivanand Bandekar is treating him. We are giving him the best medical care, the chief minister said.
Health Minister Vishwajit Rane said another medical team is on a standby to ensure best treatment for Naik.
Rane tweeted Really shocked to hear about the news of Shri @shripadynaik Jis car accident.
"Our team of doctors at Goa Medical College and Hospital are on standby to ensure the best treatment for his recuperation. Shall be personally monitoring the same.
In yet another tweet, Rane said Deeply saddened to hear about the sad demise of Smt Vijaya Naik Ji, wife of Shri Shripad Naik Ji.
"I extend my heartfelt condolences to the bereaved family. May her soul rest in eternal peace."